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Nat Commun. 2012 Jan 24;3:641. doi: 10.1038/ncomms1653.

An exactly solvable model for the integrability-chaos transition in rough quantum billiards.

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Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.

Erratum in

  • Nat Commun. 2013;4:1458.


A central question of dynamics, largely open in the quantum case, is to what extent it erases a system's memory of its initial properties. Here we present a simple statistically solvable quantum model describing this memory loss across an integrability-chaos transition under a perturbation obeying no selection rules. From the perspective of quantum localization-delocalization on the lattice of quantum numbers, we are dealing with a situation where every lattice site is coupled to every other site with the same strength, on average. The model also rigorously justifies a similar set of relationships, recently proposed in the context of two short-range-interacting ultracold atoms in a harmonic waveguide. Application of our model to an ensemble of uncorrelated impurities on a rectangular lattice gives good agreement with ab initio numerics.


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